Confidence in erosion model predictions is crucial for their effective use in design and operation of pipelines in upstream oil and gas industry. Accurate and precise estimates of the model discrepancy would increase the confidence in these predictions. We developed a Gaussian process (GP) model based framework to estimate erosion model discrepancy and its confidence interval. GP modeling, as a kernel-based approach, relies on the proper selection of hyperparameters. They are generally determined using the maximum marginal likelihood. Here, we present a bi-objective optimization approach, which uses minimization of mean squared error (MSE) and prediction variance (VAR) for training GP models. For this application, GP models trained using bi-objective optimization yielded lower MSE and VAR values than the ones trained using the maximum marginal likelihood. This paper is an extended version of a conference paper (Wei et al., 2018) presented at the 13th International Symposium on Process Systems Engineering. (C) 2019 Elsevier Ltd. All rights reserved.